摘要
本文是从拓扑学的角度来看覆盖广义粗集理论,先引进拓扑空间的相对内部和相对闭包的概念并对其进行了较深入的研究,主要结果有,(1)相对内部和相对闭包的基本性质;(2)同一拓扑的两个子基生成相同的相对内部和相对闭包的充分必要条件;(3)相对内部运算和相对闭包运算的公理化。这些结果可以看作是覆盖广义粗集的理论基础,同时对于覆盖广义粗集理论的研究也提供了一种尝试的方法。
In this paper we define relative interior and closure operators in a topological space and study them further, and obtain the following results : ( 1 ) Properties of relative interior and closure operators ; ( 2 ) Necessary and sufficient condition for relative interior and relative closure, generated by two subbases of the same topological space , to be the same , respectively ; ( 3 ) The axiomatization of relative interior operator and relative closure operator. Those results can be considered as the theory foundation of the covering generalized rough sets, at the same time, they afford a method to study the covering generalized rough sets.
出处
《模式识别与人工智能》
EI
CSCD
北大核心
2004年第1期7-10,共4页
Pattern Recognition and Artificial Intelligence
基金
国家自然科学基金(No.10271056)
